The first of these identities is due to Stade [1]}, while the second follows readily by appealing to the fact that \(\psi _\lambda (x) = \psi _{-\lambda }(x^{\prime })\)  where \(x^{\prime } = -x_{N-i+1}\) . They also follow from [2]} once one observes that the multiplicative Whittaker functions \(\Psi ^N_{\lambda }(x)\)  in [2]} are related to those defined above via \(\Psi ^N_{\lambda }(x) = \psi _{I\lambda }(\log x)\) , with \(\log x = (\log x_1,\ldots ,\log x_N)\) .
